First, it’s true that most illegal immigrants are not imprisoned for committing additional crimes (beyond coming here illegally) in the United States. One might fairly deduce that most are otherwise law-abiding. But “criminal aliens” — those who engage in other criminal acts — do make up a disproportionate number of inmates in our prisons and jails. Seeing the numbers, one might fairly deduce that they commit serious crimes at a significantly higher rate than those in the U.S. legally.

Here’s how the latest numbers break down.

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The U.S. population is around 328 million. It’s estimated that about 11 million — or one in 30 — are illegal immigrants. Yet criminal aliens account for more than one in five federal prison inmates. Even assuming a pretty radical margin of error for the sake of argument, that would still mean illegal immigrants are drastically over-represented among the criminal population.

And the actual picture may be worse, since the government says it has no way to be notified of all imprisoned illegal immigrants. So, instead, it counts a subset of them that it learns about through identifiers such as an FBI number.

The latest information is included in a recent report from the Government Accountability Office (GAO). The summary by the leader of GAO’s Homeland Security and Justice team, Gretta Goodwin, seems oddly written to try to put a positive spin on the grim findings. It highlights this figure: From 2011 through 2016, the criminal alien proportion of the total estimated federal inmate population generally decreased, from about 25 percent to 21 percent.

Stop there and you might think we’re on a good path. But dig into the actual report and footnotes — and it’s difficult to sugarcoat the findings.

There were more than 730,000 criminal aliens in U.S. or state prisons and local jails during the period measured. They accounted for 4.9 million arrests for 7.5 million offenses. (The numbers, according to the GAO: 197,000 criminal aliens in federal prisons, arrested 1.4 million times for 2 million offenses, between 2011 and 2016; 533,000 in state or local facilities between 2010 and 2015, representing 3.5 million arrests for 5.5 million offenses.)

The arrests include allegations of more than 1 million drug crimes, a half-million assaults, 133,800 sex offenses and 24,200 kidnappings. Even more serious, the imprisoned illegal immigrants, over a five-year period, had been arrested for 33,300 homicide-related offenses and 1,500 terrorism-related crimes.

In terms of cost, federal taxpayers shelled out more than $15 billion during the period studied — or $2.5 billion a year — to keep criminal aliens behind bars in federal, state and local facilities.

Many are repeat offenders. Of about 146,500 criminal aliens who finished a federal prison term, about one in six — around 24,800 — already had been imprisoned again at least once.

Why hasn’t this made headlines? It could be the way the GAO presented the results as a positive improvement. It took me some time to sort through and analyze what was really being reported. In addition, though they squabble publicly, some among both major political parties have a vested interest in keeping the status quo. Even when a single party has held both houses of Congress and the presidency, they haven’t really changed much to address illegal immigration one way or another.

If politicians ever truly get serious about reforming our immigration system — whether it’s offering legal status to illegal immigrants and allowing more to come into the United States, or tightening the borders and enforcing existing laws to deport those who technically aren’t allowed — it would seem either process should start with an honest look at the stats.

Sharyl Attkisson (@SharylAttkisson) is an Emmy Award-winning investigative journalist, author of The New York Times bestsellers “The Smear” and “Stonewalled,” and host of Sinclair’s Sunday TV program, “Full Measure.”